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Questions tagged [wolfram-alpha]

For mathematical questions related to the usage of WolframAlpha.

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Analysis of a deceptively simple infinite product: $f(n) = \prod_{j=2}^{\infty}\left(1-\frac{1}{j^n}\right)$

I am reading the book "An introduction to Infinite Product" by Charles H. C. Little , Kee L. Teo and Bruce van Brunt (https://doi.org/10.1007/978-3-030-90646-7). The book mentions the ...
Minh Đức Hoàng's user avatar
29 votes
4 answers
4k views

Why does a product $\lim_{n\to\infty} \prod_{i=1}^n (1- \frac{1}{n+2i})$ lead to infinity?

I asked Wolfram Alpha to compute the following limit: $\lim_{n\to\infty} \prod_{i=1}^n (1- \frac{1}{n+2i})$ and the answer was $\infty$. I do not understand how this can be, as all elements in the ...
Erel Segal-Halevi's user avatar
0 votes
1 answer
117 views

Why won't Wolfram Alpha compute my Limit? [closed]

Wolfram input: ...
Sectever's user avatar
5 votes
1 answer
981 views

Why does Wolfram Alpha give two different, inconsistent answers for sum of a matrix?

I would like to find out what $\sum_{r=1}^{n} \pmatrix{1 & -1 \\ 0 & 2}^r$ is equal to. I have typed this expression into WolramAlpha twice and got a different answer each time, both ...
PhysicsMathsLove's user avatar
2 votes
2 answers
50 views

Steps WA used to simplify $\left( \frac{\cos \beta \sin \beta \cos\phi +\sin \beta}{\sin^2 \phi + \sin^2\beta \cos^2 \phi} \right)^2\cos \phi$

I have the following expression: $$\left( \frac{\cos \beta \sin \beta \cos\phi +\sin \beta}{\sin^2 \phi + \sin^2\beta \cos^2 \phi} \right)^2\cos \phi$$ Wolfram Alpha yields a simplified form of this ...
rdemo's user avatar
  • 317
3 votes
1 answer
119 views

Why does Wolfram Alpha give a wrong answer to a linear ODE with constant coefficients?

This is very odd as it is a really simple ODE and the interpretation of the input seems correct, yet Wolfram Alpha produces rubbish: $$x'' - 2x' + x = t, \quad x(0) = 1.$$ Wolfram Alpha claims that ...
Klaus's user avatar
  • 10.6k
18 votes
1 answer
418 views

How does Wolfram find the closed form of numbers?

Introduction I don't know if this question has already been asked (I didn't find it in the list of questions already asked) and I hope it won't be closed immediately since it's technically a question ...
Efesto's user avatar
  • 1
0 votes
2 answers
202 views

How to integrate to get sinh? (Wolfram Alpha)

I am currently trying to find the curve that a surfer makes in attempting to get to beyond where the waves break while a current pushes against him perpendicularly, and am using this post as help: ...
Mr_Ryder's user avatar
1 vote
2 answers
110 views

$\int_{|z| = 2 }\frac{4z^7-1}{z^8-2z+1} dz= ?$

Problem: Compute $\int_{|z|=2} \frac{4z^7 - 1}{z^8 - 2z + 1}dz$. Attempt: I notice that if $w = z^8 - 2z + 1$ then $dw = 2 (4z^8 - 1) dz$ so $$I=\int_{|z|=2} \frac{4z^7 - 1}{z^8 - 2z + 1}dz = \frac{1}{...
mathlover314's user avatar
1 vote
1 answer
79 views

Contradiction occurred trying to calculate the value of $\sqrt{2}+Re\Bigl(^{10}\hspace{-1mm}\left(-\sqrt{2}\right)\Bigr)$ [closed]

Today I was trying to calculate the value of $\sqrt{2}+Re\Bigl(^{10}\hspace{-1mm}\left(-\sqrt{2}\right)\Bigr)$ (i.e., $\sqrt{2}$ plus the real part of the tenth tetration of the base $-\sqrt{2}$) up ...
Marco Ripà's user avatar
  • 1,112
0 votes
0 answers
55 views

Conformal Maps of Quaternions

When we use the wolframalpha to plot a complex function, like $$f \left( z \right) = e^z, \text{ } z \in \mathbb{C}$$ , the program show us the conformal map, that take vertical and horizontal lines ...
Gabriel Fanini's user avatar
4 votes
1 answer
159 views

Why do CAS struggle with $\int\frac{dx}{1+\sinh x}$?

$\int\frac{dx}{1+\sinh x}$ is a slightly annoying but still easily solved integral using a weierstrass substitution and PFD. I'm mainly referring to WolframAlpha, but I've seen other computer algebra ...
Nathan29006781's user avatar
18 votes
2 answers
896 views

Trying to calculate a limit with a finite product and WolframAlpha disagrees with my logic.

I want to calculate $$\lim_{N \to \infty} \prod_{j=1}^{N} \frac{2j}{N + j + 1} \,.$$ Here is my logic: For the range of the product operator ($1 \leq j \leq N $) the inequality $2j < N + j + 1$ is ...
Jose's user avatar
  • 484
4 votes
1 answer
170 views

How to integrate $\int \frac{1}{\sqrt{x+1}-\sqrt{x+3}+\sqrt{x+5}}dx$?

How to integrate $$\int \frac{1}{\sqrt{x+1}-\sqrt{x+3}+\sqrt{x+5}}dx$$. In my school life , I learnt how to integrate $$\int \frac{1}{\sqrt{x+a}-\sqrt{x+b}}dx$$ or $$\int \frac{1}{\sqrt{x+a}+\sqrt{x+b}...
Syamaprasad Chakrabarti's user avatar
1 vote
0 answers
62 views

Plot a piece of a spherical shell - Wolfram Alpha website

I'd like to know how to plot a piece of a spherical shell $0.118<r<0.236$, $0<\theta<\pi$, $0<\phi<\pi/2$ by using the website Wolfram Alpha.
Gennaro Arguzzi's user avatar
1 vote
1 answer
130 views

How to obtain a recurrence relation for Taylor series coefficients?

Recently, I asked WolframAlpha to give me the first few terms in the Taylor series for a complicated (but well-behaved) function. It did so, but also provided a recurrence relation for the ...
dank's user avatar
  • 13
1 vote
1 answer
91 views

Ambiguous solution of Integral in Wolfram Alpha

Wolfram Alpha gave me a solution to an integration that needs consecutive substitution, where I do not understand how to make a definite decision on which function should be u and which du. $$\int x \...
lemma25's user avatar
  • 11
3 votes
3 answers
232 views

Desmos and Wolfram Alpha contradict: Is $|1+x| \ge 1 - |x|$ true for all $x$?

Is $|1+x| \ge 1 - |x|$ true for all $x$? When I solve this problem myself, I solved that it's true for all $x$. But when I put it into Desmos, I get this: https://www.desmos.com/calculator/vgxm3q1fso,...
mathmuffin's user avatar
2 votes
2 answers
199 views

Why does Desmos not plot $ \sqrt{\frac{(x+y)^2}{2}} = \sqrt{x^2+y^2} + \sqrt{2} $?

I am working on the following problem: I need to find the points above the line $l:y=-x$ for which it holds that the distance to $l$ is $\sqrt{2}$ greater than the distance to the origin. I worked out ...
UnrulyTank's user avatar
0 votes
2 answers
62 views

$(x - \frac{\pi}{2}) (x - \frac{3\pi}{2})(2-tan(x)) $ does not share roots with $(x - \frac{\pi}{2}) (x - \frac{3\pi}{2})$. Why?

I was practicing for my trig test, and I came across this question $2\cos(x) - \sin(x) = 0$. I tried applying the trig identity $\tan(x) = \frac{\sin(x)}{\cos(x)}$ resulting in the following equation: ...
servr cube's user avatar
1 vote
1 answer
65 views

Integration of the function derivative wrt the function

According to wolframalpha $$ \int f'(x)df(x) = f'(x) f(x) + constant $$ I am trying to get the RHS, but alas... I tried to apply integration by parts and to apply it twice
Green.H's user avatar
  • 1,201
4 votes
0 answers
80 views

Wolfram wishlist: series of $\Gamma(z)$ in $z=-m$. Cycle index of symmetric groups.

I found out that Wolfram has a wish list of formulas it is researching. The first point is "Series for the gamma function" We are searching for general formulas for the series expansion of ...
Math Attack's user avatar
1 vote
2 answers
93 views

Definite integral $\int_{-\infty}^\infty \int_{-\infty}^\infty \exp(-x^2 y^2) \; dx dy$?

The deceptively simple-looking double integral $$ \int_{-\infty}^\infty \int_{-\infty}^\infty \exp(-x^2 y^2) \; dx dy $$ is clearly finite, but both maple and Wolphram alpha gives the value $\infty$...
kjetil b halvorsen's user avatar
1 vote
1 answer
306 views

Difference in differentiation between Mathematica and Wolfram Alpha

I am trying to differentiate this: $$f(x)=e^{-x^2}$$ In Wolfram Alpha I get this: $$-2x\,e^{-x^2}$$ But in Mathematica I get: $$-2x\,e^{-x^2}\log(e)$$ Why the difference?
user1078's user avatar
  • 341
0 votes
1 answer
45 views

Discrepancy wolfram alpha and hand calculation of a gaussian integral

Wolfram alpha gives me the following result: $$ \int_0^{+\infty} \frac{x^2\, e^{-a x^2}}{\sqrt{x^2 +m^2}}\, dx = \frac{\sqrt{\pi}}{4 a} U\Big(\frac{1}{2},0, a m^2 \Big)$$ and it does use the usual ...
Noix07's user avatar
  • 3,569
2 votes
0 answers
38 views

How do I find the constants in this differential equation that describes the time taken for a bubble to rise to the surface.

I'm trying to model the behaviour of bubbles in a water column as accurately as I'm able to, and I modelled a Differential equation using F = ma and a free body diagram. The equation of motion I ...
Movin Jayasinha's user avatar
0 votes
0 answers
31 views

FindRoot error in NDSolve

I have two coupled differential equations as follows \begin{eqnarray} \frac{\partial }{\partial x}U[x,y] &=&2V[x,y], \notag \\ \frac{\partial }{\partial y}V[x,y] &=&V[x,y]U[x,y]+1, \...
A.D's user avatar
  • 19
2 votes
2 answers
67 views

Domain of $\frac{1}{x^{-1}}$

Why WolframAlpha and other online calculators compute $x\in \mathbb{R}-\{0\}$ (and not $\mathbb{R}$) as the domain of $\frac{1}{x^{-1}}$? Since $\frac{1}{x^{-1}}=\frac{1}{\frac{1}{x}}=x$, is not the ...
rik's user avatar
  • 79
0 votes
0 answers
65 views

Rationality of artan(2/pi)

I was messing around on Wolfram Alpha and I saw that the conversion of arctan(2/pi) from radians to degrees was 32.48. Wolfram Alpha usually shows more decimal spaces, so I was wondering where this is ...
Dhairya Pandya's user avatar
5 votes
2 answers
211 views

Why Wolfram gives inconsistent result for: $\int_0^\infty \frac{e^{x-x^2}-e^{-x-x^2}}{x}~dx$

Why Wolfram gives inconsistent result for : $$I=\int_0^\infty \frac{e^{x-x^2}-e^{-x-x^2}}{x}~dx$$ As shown in the picture below, the analytical integration gives $-i\pi$, but numerical integration ...
MathFail's user avatar
  • 21.2k
1 vote
2 answers
263 views

Does this Fourier Legendre series inverting $\frac65\frac{x^x}{x+1}-\frac35$ diverge or it is a software issue past $\approx 25$ series terms?

$\def\P{\operatorname P}$ The goal of the Fourier Legendre series is to find an exact explicit series solution to $x^x=x+1$, not just $x=a+b+c+\dots$ with unknown series coefficients. Lagrange ...
Тyma Gaidash ٠'s user avatar
2 votes
1 answer
76 views

How does Wolfram|Alpha derive direct formulas for $\sum_{k=0}^nk^m$? [duplicate]

I'm curious as to how Wolfram|Alpha manages to derive a direct formula for summations of powers, such as the classic $\sum\limits_{k=0}^n k^2$, or more difficult ones such as $\sum\limits_{k=10}^{n} k^...
kwyntes's user avatar
  • 121
15 votes
3 answers
800 views

Evaluate $\int_{-\infty}^\infty \frac{\sin{(x\sin{x})}}{x^2}dx$.

Evaluate $$\int_{-\infty}^\infty \frac{\sin{(x\sin{x})}}{x^2}dx.$$ Numerical investigation suggests that it equals $\pi$. Let $f(\alpha)=\frac{1}{\pi}\int_{-\alpha}^\alpha \frac{\sin{(x\sin{x})}}{x^2}...
Dan's user avatar
  • 23.7k
0 votes
1 answer
100 views

How to evaluate $\displaystyle \int_0^{\frac{\pi}{2}}\ln(1+\sin(t)^2)\mathrm{d}t$ [duplicate]

I'm struggling with this integral, I've tried different substitutions but i can't solve it. $$\displaystyle \int_0^{\frac{\pi}{2}}\ln(1+\sin(t)^2)\mathrm{d}t$$ I've tried to calculate both the ...
user avatar
0 votes
1 answer
57 views

Feeding parameters into a multivar function in Mathematica

I am trying to find an intersection point between a plane and a line. I defined my line as a function of $x,y$ and $z$. g[x_, y_, z_] := 5 x - 8 y + 2 z - 13 I ...
Jakob's user avatar
  • 15
2 votes
0 answers
40 views

Wolfram says series is divergent, how is my proof wrong? [duplicate]

Given the following series Wolfram Alpha says it diverges but when I was trying to prove it I came to the conclusion it converges and I can't figure out what's wrong. $$\sum_{n=2}^\infty \frac{(-1)^n}{...
Ivan's user avatar
  • 21
1 vote
3 answers
111 views

Value of $x$ such that the area under the curve of $lnx$ up to $x$ is $1$.

This value would be the solution to:$$\int_{0}^{a}\ln(x)dx=1$$ With integration by parts this is well known to be $[x\ln(x)-x]^a_0=1$ or what is the same:$$a\ln(a)-a=1$$ The limit at $0$ easily ...
RealityIsSenseless's user avatar
2 votes
2 answers
193 views

Can you help me understand the properties and zeros of this function involving square roots terms?

Consider this function ( I got this when I was solving an another problem) f(n) = $$\left(\frac{1}{2}\right)\left[\left(\frac{n^2+\sqrt{n^4+16008n}}{2n}\right)+\sqrt{\left(\left(\frac{n^2+\sqrt{n^4+...
The Safe's user avatar
1 vote
1 answer
166 views

Closed form solution $\sum\limits_{n=1}^{\infty}\frac{\left(-1\right)^{n}}{H_n}$

$$\sum\limits_{n=1}^{\infty}\frac{\left(-1\right)^{n}}{H_n}$$ Where $H_n$ denotes the nth harmonic number. I am a little confused because WolframAlpha says here that it is approximately $-0.626332$ ...
Dylan Levine's user avatar
  • 1,666
2 votes
1 answer
99 views

WolframAlpha syntax - evaluate series at a point

I am looking for syntax for WolframAlpha, which would evaluate a series at a given point. My goal is to have a sheet of practice exercises with links to solutions in WolframAlpha. Example problem: ...
Lukáš Mrazík's user avatar
0 votes
1 answer
101 views

Solve a 2D linear recurrence

I need to know the solution of this recurrence: $$2a[n,k-1]-a[n-1,k-1]-2a[n-1,k-2]+a[n-2,k-2]=a[n,k]$$ With the initial value unspecified. Also, wolfram is good at solving linear 1D recurrence, but ...
Austin Chen's user avatar
2 votes
0 answers
276 views

PDF or CDF of the sum of two Weibull random variables with shape parameter 1/2

I saw that the pdf of the sum of two independent Weibull random variables is not known in general. However, in the case of 'shape parameter = 1/2' in both variables, is there a closed-form expression ...
BHB's user avatar
  • 21
-3 votes
1 answer
102 views

How can i use Maple(or any other software) to rearrange any equation into another equation? [closed]

Let's say I have some equation $= x^2+y=3$. I want to somehow rearrange this into something else such as $x=({\rm root}(3-y) z)/z$. I solved for x and multiplied z above and below. Can Maple (or some ...
Damon Kutt's user avatar
0 votes
1 answer
58 views

Deriving CI for the mean: Wolfram Alpha giving different answer for equation and inequality [closed]

As a simple example, say I'm trying to derive the upper bound of a confidence interval for the mean. That is, I'm trying to solve for $\mu$ in $$ \frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt{n}}} < Z_{\...
user1205901 - Слава Україні's user avatar
2 votes
0 answers
185 views

Wolfram Mathematica: why is the plot not visible?

simple question regarding Wolfram Mathematica: Why is the plot not showing? (See screenshot) (I am new to Wolfram Mathematica) Thankful for any input.
JosefS's user avatar
  • 67
1 vote
0 answers
96 views

How are person curves created?

One can graph some person curves such as Joe Biden curve and Kim Jung Un Curve using WolframAlpha. I am curious how these curves were created using parametric equations.
Zuriel's user avatar
  • 5,361
0 votes
2 answers
139 views

Discrepancy in value of $\int_0^\frac\pi2 \delta(\tan(t)-xt)dt$

The goal would have been for the smallest positive solution of $y\cot(y)=x$ using a Dirac $\delta(x)$ Fourier series and the Bateman function: $$y\cot(y)=x\mathop\implies^?\frac1{\sec^2(y)-x}=\int_0^\...
Тyma Gaidash ٠'s user avatar
0 votes
1 answer
58 views

Solving system of equations for trig problem in Wolfram Alpha

I'm new to Wolfram Alpha. I'm trying to learn how to do solving using a basic trig system of equations but I don't understand the ouput. The problem is stated in graphic below, I want to solve for t ...
David's user avatar
  • 101
0 votes
1 answer
63 views

HessianMatrix (norm[2](x)) in Wolfram

I'm very new to Wolfram-alpha. I'm trying to compute the Hessian Matrix of ||x|| where x is a vector. I tried this command HessianMatrix (norm[2][x]) in mathematica 13 where I use Wolframalpha input ...
Tomer's user avatar
  • 436
2 votes
1 answer
116 views

Why is $i$ here?

So I was trying to put $$\sum_{n=2}^\infty\frac{(-1)^n}{\pi(n)}$$(where $\pi(n)$ is the prime counting function) into Wolfram Alpha. It didn't work. So I decided to replace $\pi(n)$ with $\ln n$. I ...
Kamal Saleh's user avatar
  • 6,542

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